The Makian Distribution
To be more precise, the distribution during periods of market stress and high leverage is likely to be a “M” shape, which I call the Makian Distribution.
For those interested in the economic theory behind the combined deflationary/inflationary highvolatility Mshaped “Makian” distribution, I give you this Austrian School analysis of the modern monetary system, which predicted the financial crisis and also predicted a combined/simultaneous deflationary/stagflationary financial crisis from which there will be no escape, other than complete destruction of the monopoly currency and an associated social implosion of the Weimar Republic kind.
The fundamental point is that the mainstream think a nice, neat, “use all the time”, “off the shelf” bell curvebased quantifiable model that has been shown not to reflect the dynamics of real markets is still “useful” because it just might (might!) approximate reality in the short run and does allow quantification (and therefore pricing) of risk. Often mainstream financial modellers admit the normal distribution is wrong, but nothing (quantifiable) is better, so we may as well use it in order to price risk in the financial markets.
There have been a few attempts at modelling using nonnormal distributions, and they have included some useful modelling of time dependency. However they haven’t gotten very far and haven’t integrated the very recent research on agency modelling which suggests that sudden changes in risk distributions are associated with levels of leverage.
I happen to believe the use of the normal distribution is worse than useless because it leads the whole financial sector to underestimate volatility during periods of high leverage and debt. An “Mshaped” distribution (which I call the “Makian distribution” for want of a better term) would at least warn people of the impending volatility when leverage hits unprecedented levels.
The technical term for this phenomenon would be “bifurcating bell curves” or “bifurcating normal distributions” where, as leverage increases, you actually see a bifurcation of the longterm normal distribution into two overlapping normal distributions, which can go either way (deflation or hyperinflation) depending solely on what the central bankers decide to do in the middle of the panic (which in itself cannot ever be quantified).
Deflation is when they panic one way, and keep the money supply reasonably stable. Hyperinflation is when they panic the other way, and try to “compensate” for lack of liquidity during a credit crunch. But one thing is clear through all the empirical history – whoever is in charge, they always panic (as 2008, 2001, 1991, 1987, 1982, 1970s, 1960s, 1930s, 1912, and the whole of the 19th century so clearly shows).
It can go either way. What is actually least likely during these periods of high leverage is the maintenance of steady growth in financial markets consistent with the longterm mean.
Taleb (sort of) understands this by saying that the modelling underestimates extreme events, but even that doesn’t capture what I’m saying. He just worries a lot, but doesn’t replace the normal distribution with anything else. With Taleb, you’re “flying blind” with the distribution really being a horizontal line across the returns spectrum. I don’t think that’s very helpful either.
No one else seems to have the required combination of skills to analyse probability and financial modelling from first principles. The academics built a huge edifice on shaky foundations because none of them studied the philosophy of probability. They shoved the normal distribution on to financial markets as a Procrustean solution that would never work because they focused on fitting a familiar model onto a messy world. Disaster!
To understand financial modelling you need to have (at minimum) the following attributes: (1) studied Mises on probability (2) studied the philosophy of probability (3) reflected on the inherently subjective nature of probability for nonreplicable events in financial markets (4) know something (anything!) about Austrian economics (5) be qualified and reasonably competent in financial modelling and mathematical econometrics.
An “M” shaped bifurcating bell curve would seem to me a neat way of combining Austrian School analysis of probability with recent agencybased models suggesting a link between volatility and leverage.
Are you in banking or finance? Do you use the normal distribution to model risk? Why?

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